Lapping is a well-established process for finishing the tooth surfaces of bevel gears. The purpose of lapping is to alter or refine gear tooth flanks to improve gearset running noise (motion transmission errors). These motion transmission errors can be characterized as short-term (once-per-tooth and harmonics thereof) and long-term (once-per-revolution run-out and harmonics thereof).
In the lapping process, members of a bevel gear set, namely a pinion and ring gear, are mounted to respective spindles in a lapping machine via appropriate workholding equipment. In most instances of rolling of the gear set during lapping, the pinion is the driving member and the ring gear is braked thereby creating an amount of torque between the pinion and ring gear. The gear members are rolled in mesh and lapping compound, which can be a mixture of oil (or water) and silicon carbide or similar abrasive, is sprayed, injected or poured into the meshing zone. In a typical lapping cycle, first one side of the gears (e.g. coast side) is lapped followed by lapping of the other side (e.g. drive side) of the gears. An example of a gear lapping machine can be found in U.S. Pat. No. 6,120,355 to Stadtfeld et al.
Most lapping machines have three degrees of freedom available for realizing relative motion between a ring gear and pinion. The first freedom being relative movement in the direction of the ring rear axis (gear cone distance) which shall be referred to as direction G or the G-axis, the second freedom being relative movement in direction of the pinion axis (pinion cone distance) which shall be referred to as direction H or the H-axis, and the third degree of freedom being distance between the ring gear and pinion axes which shall be referred to as direction V or the V-axis. The direction V is also known as the “hypoid offset” or “pinion offset.”
In lapping processes, relative movement in the V, H and G directions effect positional changes in the contact pattern of the members of the gear set, in effect modifying the contact pattern. Lapping involves rotating the gear members in mesh with contact at a desired position on the tooth surfaces. Thus, the members are located at particular V and H positions along with a particular G-axis position to effect the desired backlash.
Typically, the V, H and G movements each have an effect on both the lengthwise and depthwise position of the localized tooth contact pattern, the primary effect of the V-axis movement being on the relative lengthwise position of the contact pattern, the primary effect of the H-axis movement being on the relative depthwise position of the contact pattern, and the primary effect of the G-axis movement being on the backlash.
As the gear set is lapped, contact is usually shifted smoothly and gradually from the center of the tooth toward one of the outer (heel) or inner (toe) portions of the tooth surface by changing the V and H settings as necessary to effect such a shifting of the contact position. As V and H are changed to effect the shifting, the G-axis position must also be changed smoothly and gradually to maintain the desired backlash. When the desired heel or toe position is reached, V and H axes positions are again changed to shift contact to the other of the heel or toe positions with the changing V and H positions being accompanied by an appropriate G-axis change to maintain backlash. The contact position is then returned to the beginning position at the center of the tooth.
Torque is developed by the machine spindle motors such that a desired speed and load are produced at the gearset, with material removal rate by abrasive action being a function of the load. The load, or gearset torque, may also have an average level determined by the user (e.g. 10 Newton-meters) when setting up the lapping job. This average torque level is maintained in-process by the machine according to various known methods, such as disclosed in U.S. Pat. No. 6,481,508 to McGlasson et al.
But the gearset torque also has dynamic components which are not actively controlled. Such dynamic components are unavoidably present as a result of machine response to gearset motion errors influenced by masses, stiffness and damping of the spindles and other machine elements (i.e. passive physics of the machine). These dynamic components, initiated primarily from the gearset motion errors, add to the average torque to comprise the actual lapping torque. Thus, at any given instant, the lapping torque may be substantially higher or lower than the commanded average value, based on these dynamics. The performance, and performance limitations, of a lapping machine is in large part dependent on these passive physics-based behaviors, and the faster the spindles are rotated during lapping, the more dominant these effects tend to become.
Therefore, significant limiting effects often arise from the passive dynamic motion/torque behavior of the lapping machine system. It has been found that lapping machine parameters (mechanical design, control characteristics and process choices) that produce the best tooth modification performance may not at the same time produce the best spacing and/or run-out performance, and vice versa. In other words, a machine design for optimal improvement in tooth flank shape may, on average, merely maintain or even make run-outs worse. And a machine designed to consistently improve part run-out may achieve sub-optimal tooth-to-tooth characteristics.
One example of addressing tooth characteristics can be found in U.S. Pat. No. 4,788,476 to Ginier where a method is disclosed for utilizing and manipulating the intermittent contact of an interference-based lapping approach (resulting from operating the two spindles in velocity and/or position modes) in order to selectively lap distorted or out-of-position gear teeth. Control of the process comes down to the timing of when to advance and when to maintain a commanded interference condition that is producing lapping torque. The resulting lapping cycle is generally too slow to be used in production and over-lapping of some teeth (rendering the gear set unusable) can be expected if pre-lapping spacing errors are significant.